Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii

Table of contents

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[171.] Scholium Generale.
Page: 194 (180)
[172.] Commentationes ſpeciales de Cochlea Archimedis.
Page: 197 (183)
[173.] Problema.
Page: 200 (186)
[174.] Solutio.
Page: 200 (186)
[175.] Scholium 1.
Page: 200 (186)
[176.] Scholium 2.
Page: 201 (187)
[177.] Scholium 3.
Page: 202 (188)
[178.] Scholium 4.
Page: 202 (188)
[179.] Problema.
Page: 203 (189)
[180.] Solutio.
Page: 203 (189)
[181.] Scholium 1.
Page: 205 (191)
[182.] Scholium 2.
Page: 205 (191)
[183.] (C) De Machinis, quæ ab impetu fluidi, veluti vi venti moventur.
Page: 207 (193)
[184.] HYDRODYNAMICÆ SECTIO DECIMA. De affectionibus atque motibus fluidorum elaſti-corum, præcipue autem aëris. §. 1.
Page: 214 (200)
[185.] Digreſsio de refractione radiorum per atmoſphæ-ram transeuntium.
Page: 233 (219)
[186.] Problema.
Page: 238 (224)
[187.] Solutio.
Page: 238 (224)
[188.] Problema.
Page: 240 (226)
[189.] Solutio.
Page: 240 (226)
[190.] Corollarium 1.
Page: 241 (227)
[191.] Corollarium 2.
Page: 241 (227)
[192.] Problema.
Page: 241 (227)
[193.] Solutio.
Page: 242 (228)
[194.] De vi aëris condenſati & auræ pulveris pyrii ac-cenſi ad globos projiciendos in uſu ſclopetorum pneumaticorum & tormentorum bellicorum.
Page: 248 (234)
[195.] HYDRODYNAMICÆ SECTIO UNDECIMA. De fluidis in vorticem actis, tum etiam de iis, quæ in vaſis motis continentur. §. 1.
Page: 258 (244)
[196.] HYDRODYNAMICÆ SECTIO DUODECIMA. Quæ ſtaticam fluidorum motorum, quam hy-draulico - ſtaticam voco, exhibet. § 1.
Page: 270 (256)
[197.] Problema.
Page: 272 (258)
[198.] Solutio.
Page: 272 (258)
[199.] Corollarium 1.
Page: 274 (260)
[200.] Corollarium 2.
Page: 274 (260)
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            <s xml:id="echoid-s7581" xml:space="preserve">
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            ficium H. </s>
            <s xml:id="echoid-s7582" xml:space="preserve">Eadem methodus inſervit ad preſſiones aquarum in reliquis vaſis,
              <lb/>
            quæ in Sectione octava tractavimus, determinandas. </s>
            <s xml:id="echoid-s7583" xml:space="preserve">Differunt autem omnes
              <lb/>
            hæ quæſtiones ab iis, quæ ad motum fluidorum per canales pertinent, quod
              <lb/>
            aquæ ob infinitam vaſorum à nobis poſitam amplitudinem veluti quieſcant in
              <lb/>
            cavitatibus & </s>
            <s xml:id="echoid-s7584" xml:space="preserve">nihilominus preſſionem longe aliam exerceant, quam aliter ſo-
              <lb/>
            lent. </s>
            <s xml:id="echoid-s7585" xml:space="preserve">In canalibus autem aquæ preſſionem ſuam eo magis mutant, quo majo-
              <lb/>
            ri velocitate præterfluunt, & </s>
            <s xml:id="echoid-s7586" xml:space="preserve">omnem fere conſuetam preſſionem exerunt, ſi
              <lb/>
            velocitas iſta ſit valde parva.</s>
            <s xml:id="echoid-s7587" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7588" xml:space="preserve">Hæc ita, cum velocitates fluidorum determinari poſſunt per methodos
              <lb/>
            jam ſuprà à nobis traditas. </s>
            <s xml:id="echoid-s7589" xml:space="preserve">Singulari autem methodo res pertractanda eſt, cum
              <lb/>
            aquæ per canales fluunt, hancque doctrinam potiſſimum titulo hydraulico-ſtati-
              <lb/>
            cæ intelligo: </s>
            <s xml:id="echoid-s7590" xml:space="preserve">Hic non tam preſſio ex velocitate quam reciproce velocitas, ſi
              <lb/>
            foraminulum in lateribus canalis fiat, ex preſſione definiri poteſt. </s>
            <s xml:id="echoid-s7591" xml:space="preserve">Et de iſta
              <lb/>
            hydraulico-statica, cujus uſus ampliſſimus eſt, in præſenti ſectione potiſſimum
              <lb/>
            agere conſtitui.</s>
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        <div xml:id="echoid-div261" type="section" level="1" n="197">
          <head xml:id="echoid-head254" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s7593" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7594" xml:space="preserve">5. </s>
            <s xml:id="echoid-s7595" xml:space="preserve">Fuerit vas ampliſſimum A C E B (Fig. </s>
            <s xml:id="echoid-s7596" xml:space="preserve">72.) </s>
            <s xml:id="echoid-s7597" xml:space="preserve">aqua conſtanter ple-
              <lb/>
              <note position="left" xlink:label="note-0272-01" xlink:href="note-0272-01a" xml:space="preserve">Fig. 72.</note>
            num conſervandum, tubo inſtructum cylindrico & </s>
            <s xml:id="echoid-s7598" xml:space="preserve">horizontali E D; </s>
            <s xml:id="echoid-s7599" xml:space="preserve">ſitque in
              <lb/>
            extremitate tubi foramen o aquas velocitate uniformi emittens; </s>
            <s xml:id="echoid-s7600" xml:space="preserve">quæritur preſſio
              <lb/>
            aquæ in latera tubi E D.</s>
            <s xml:id="echoid-s7601" xml:space="preserve"/>
          </p>
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          <head xml:id="echoid-head255" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s7602" xml:space="preserve">Sit altitudo ſuperficiei aqueæ A B ſupra orificium o = a; </s>
            <s xml:id="echoid-s7603" xml:space="preserve">erit velocitas
              <unsure/>
              <lb/>
            aquæ in o effluentis, ſi prima fluxus momenta excipias, uniformis cenſenda
              <lb/>
            & </s>
            <s xml:id="echoid-s7604" xml:space="preserve">= √a, quia vas conſtanter plenum conſervari aſſumimus; </s>
            <s xml:id="echoid-s7605" xml:space="preserve">poſitaque ratio-
              <lb/>
            ne amplitudinum tubi ejusque foraminis = {n/1}, erit velocitas aquæ in tu-
              <lb/>
            bo = {√a/n}: </s>
            <s xml:id="echoid-s7606" xml:space="preserve">Si vero omne fundum F D abeſſet, foret velocitas ultima aquæ in
              <lb/>
            eodem tubo = √a, quæ major eſt quam a; </s>
            <s xml:id="echoid-s7607" xml:space="preserve">Igitur aqua in tubo tendit ad ma-
              <lb/>
            jorem motum, niſus autem ejus ab appoſito fundo F D impeditur: </s>
            <s xml:id="echoid-s7608" xml:space="preserve">Ab hoc
              <lb/>
            niſu & </s>
            <s xml:id="echoid-s7609" xml:space="preserve">reniſu comprimitur aqua, quæ ipſa compreſſio coërcetur à lateribus
              <lb/>
            tubi, hæcque proinde ſimilem preſſionem ſuſtinent. </s>
            <s xml:id="echoid-s7610" xml:space="preserve">Apparet ſic </s>
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